"Lagrangian Disks" in M-theory

TL;DR

This paper explores the geometry of special Lagrangian submanifolds with boundary on complex surfaces, relating it to $G_2$ and $Spin(7)$ geometries, and proposes new brane models in type IIA string theory.

Contribution

It introduces a novel problem involving special Lagrangian boundaries, connecting it to advanced geometric structures and proposing new physical brane models.

Findings

Establishes a link between Lagrangian boundary problems and $G_2$, $Spin(7)$ geometries.

Proposes a large class of new brane models in type IIA string theory.

Relates mathematical structures to physical theories like brane brick models and 2d theories.

Abstract

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in $G_2$ holonomy spaces and to $Spin(7)$ metrics on 8-manifolds with $T^2$ fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories $T[M_4]$ on the other.